Colin Johnson’s blog

Sorites at Small Scale

The sorites (Greek for “heap”) paradox is a puzzle about language. We unambiguously use the word “heap” to represent a large pile of, say, stones—say a few hundred. If we remove one, that is still, uncomplicatedly, a heap. Yet, we cannot do this indefinitely. Once we have, say, two stones, everyone agrees that this is clearly not a heap. The usual resolution to this is to argue that concepts such as “heap” are irreducibly vague; there will always be a fuzzy middle ground between “heap” and “non-heap”.

Interestingly, there are still examples of this at very small scales. There is currently a proposal to merge two of the small number of supermarket chains in the UK. At present, most people would agree that the current system is decently competitive. Reduce is by one and—well, is it still a competitive system? Interestingly, this shows that a sorites-like situation can exist with small numbers of objects, and so perhaps isn’t a problem of fine-grainedness as much as we might first think.